# Questions tagged [density-operator]

The density operator describes a quantum system in an (in general mixed) state.

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### How can I write a Gaussian state as a squeezed, displaced thermal state

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} \hat{D}^\...
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### How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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### Green functions and density matrix

tl;dr The single particle density matrix is directly related to NEGF as shown here, I wish to find a way to relate NEGF also to density matrices which describe probability distribution of many body ...
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### Reasoning Check: Trace of squared mixed-state density matrix

It's often written in the QI literature that, for a density operator $\rho$, if $\text{Tr}\left[\rho^{2}\right] < 1$, then $\rho$ describes a mixed state. However, I haven't seen any proofs of this ...
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### Quantum master equation and off diagonal terms

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used to ...
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### Density matrix and entangled states

I am studying the density matrix formalism. I gather that: the trace of a density matrix, $tr(\rho)$ is always 1, if $tr(\rho^2) < 1$ we have a mixed state, otherwise a pure state, if $\rho$ ...
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### Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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### What is the link between the density matrix and Hestenes' spinors in geometric algebra?

The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are ...
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### Expanding a density matrix in terms of operators

In Lukasz's paper: https://arxiv.org/pdf/0909.2654.pdf He writes "consider a density matrix ρ, written as a polynomial of the 2N Majoranas cj in such a way that each cj occurs to the power 0 or 1 in ...
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### Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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### Density matrix in quantum computation and quantum statistical mechanics

What is the difference between the density matrix for quantum statistical mechanics and density matrix for quantum information theory?